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A325469 a(n) is the number of divisors d of n such that d divides sigma(d).

%I A325469 #24 Apr 18 2025 10:59:29
%S A325469 1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,
%T A325469 1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,2,1,1,
%U A325469 1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1
%N A325469 a(n) is the number of divisors d of n such that d divides sigma(d).
%C A325469 Sequence of the smallest numbers m with n divisors d such that d divides sigma(d) for n >= 1: 1, 6, 84, 672, 3360, 30240, 393120, ...
%H A325469 Antti Karttunen, <a href="/A325469/b325469.txt">Table of n, a(n) for n = 1..16384</a>
%H A325469 Antti Karttunen, <a href="/A325469/a325469.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A325469 a(A097603(n)) > 1.
%F A325469 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A335830. - _Amiram Eldar_, Apr 16 2025
%e A325469 For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d): 1, 3, 4, 7, 12, 28; d divides sigma(d) for 2 divisors d: 1 and 6; a(12) = 2.
%t A325469 a[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[1, #], #] &];  Array[a, 100] (* _Amiram Eldar_, Aug 17 2019 *)
%o A325469 (Magma) [#[d: d in Divisors(n) | IsIntegral(SumOfDivisors(d) / d)] : n in [1..100]];
%o A325469 (PARI) a(n)={sumdiv(n, d, sigma(d) % d == 0)} \\ _Andrew Howroyd_, Aug 16 2019
%Y A325469 Cf. A000203, A097603, A325470, A325471, A335830.
%K A325469 nonn
%O A325469 1,6
%A A325469 _Jaroslav Krizek_, Aug 16 2019
%E A325469 More terms from _Antti Karttunen_, Aug 22 2019